Explore chapters and articles related to this topic
Eigenlogic
Published in Sergio Barile, Raul Espejo, Igor Perko, Marialuisa Saviano, Francesco Caputo, Cybernetics and Systems, 2018
This approach is then applied in the context of quantum robots using simple behavioral agents represented by Braitenberg vehicles. Processing with non-classical logic such as multivalued logic, fuzzy logic and the quantum Eigenlogic permit to enlarge the behavior possibilities and the associated decisions of these simple agents.
Of gaps, gluts, and God's ability to change the past
Published in Journal of Applied Non-Classical Logics, 2022
Finally, there is also the general worry about whether these non-standard solutions (based on non-classical logics) truly apply to these puzzling religious doctrines. That is, is it the case that such doctrines are amenable to a non-classical treatment? To this, Beall and Cotnoir (2017) have a reply: ‘standard doctrine does not dictate that God demands classical logic; it is compatible with non-classical logic’. We could make the case stronger: a logical framework (classical or otherwise) must not dictate doctrine. To make sense of the logical ramifications of a doctrine, we have to treat it like any other target (natural language) phenomenon that we could model using a given logical framework (Beall & Logan, 2017). If the doctrine could be modelled using the classical framework, then so be it. But if it requires a non-classical framework, then we must be open to this possibility.12 This is not to say that any logical framework may be used to model any religious doctrine. After all, as with any model, we must test whether the chosen logical framework is adequate to account for the logical ramifications of the target phenomenon (Priest, 2019). That is, we evaluate its simplicity, metaphysical assumptions, explanatory power, and other theoretical virtues.
Binary Soft Connected Spaces and an Application of Binary Soft Sets in Decision Making Problem
Published in Fuzzy Information and Engineering, 2019
During the study towards possible applications in classical and non classical logic, binary soft sets and binary soft topology is very important. Nowadays, researchers daily deal with the complexities of modelling uncertain data in economics, engineering, environmental science, sociology, medical science, and many other fields. Classical methods are not always successful due to the reason that uncertainties appearing in these domains may be of various types. Zadeh [1] initiated a new approach of fuzzy set theory, which proved to be the most appropriate framework for dealing with uncertainties. While probability theory, rough sets [2], and other mathematical tools are considered as a useful approaches to describe uncertainty. Each of these theories has its own inherent difficulties as pointed out by Molodtsov [3]. Molodtsov [3,4] proposed a completely new elegant approach of soft sets theory for modelling vagueness and uncertainty which is free from the difficulties affecting existing methods. In soft set theory the problem of setting the membership function, among other related problems, simply does not arise. Soft sets are considered as neighbourhood systems, and are a special case of context-dependent fuzzy sets. Soft set theory has potential applications in many different fields, including the smoothness of functions, game theory, operations research, Riemann integration, Perron integration, probability theory, and measurement theory.
A basic quasi-Boolean logic of intuitionistic character
Published in Journal of Applied Non-Classical Logics, 2020
Well then, now it is important to remark that Sylvan and Plumwood's Minimal De Morgan logic B is the minimal logic interpretable with RM-semantics (cf. Robles & Méndez, 2018; Routley et al., 1982; Sylvan & Plumwood, 2003). Therefore, we will investigate in the sequel the logic Hb, the minimal extension of B with H-negation, and a wealth of extensions of Hb. Concerning these Hb-extensions, we will concentrate on two logics and their subsystems: Gödelian 3-valued logic G3 and H-negation expansion of the 3-valued extension of Lewis' positive modal logic S5, S5 (cf. Definitions A.2–A.4 in the Appendix). But these two strong logics and many of their subsystems are here treated as a way of an example of how to use the RM-semantics defined in the paper to interpret many other (possibly interesting) extensions of Hb endowed with the type of H-negation we have modelled (in this sense, the paper can be seen as a study on applied non-classical logic). Of course, in none of these logics are the DNE and CPEM axioms provable (cf. the Appendix), but the ECQ axiom and the axiom ‘Double Negation Introduction’ (DNI), , are theorems in all of them (cf. Proposition 2.7). Also, it has to be remarked that the ‘Principle of Excluded Middle’ (PEM), , intuitionism's bête noire, is a theorem of some of the logics included in S5. Unreduced Routley-Meyer ternary relational semantics is defined for each one of the logics introduced in the paper (cf. Brady, 2003; Routley et al., 1982 and references therein; cf. also Section 6).